Abstract: We consider the topological dynamics of the automorphism group of a particular sparse graph M_1 resulting from an ab initio Hrushovski construction. We show that minimal subflows of the flow of linear orders on M_1 have all orbits meagre, partially answering a question of T. Tsankov regarding results of D. M. Evans, J. Hubička and J. Nešetřil on the topological dynamics of automorphism groups of sparse graphs.
Keywords: sparse graph; Hrushovski construction; admissible order; meagre orbit; orientation
DOI: DOI 10.14712/1213-7243.2025.014
AMS Subject Classification: 03C15 37B05 20B27 05C55 05D10